Upload
elwin-dawson
View
220
Download
0
Embed Size (px)
Citation preview
Add, Subtract, and Multiply Matrices
A matrix M is an array of cell entries (mrow,column) that have rectangular dimensions (Rows x Columns).
Example:
2
5 17 2 20
5 0 6 15
21 10
r
M x
r t g
3x4 2,4 :m
3
4
15xDimensions:
Aarow,column
A
2,4 :a
Matrix
Scalar Multiplication
3 2 54
8 3 1
12 8 20
32 12 4
Every entry in the matrix is multiplied by the number outside the matrix (scalar).
Example:
Matrix Addition/SubtractionIF the matrices have the same dimensions, add
or subtract corresponding cell entries.
Examples:
a b c g h i
d e f j k l
a g b h c i
d j e k f l
5 3
12 0
4 10
5 3
12 0
4 10
b+h
8
12
14
Matrix Addition/Subtraction
Perform the indicated operation:
3 0.4 0
8 7 4 18 2
z w
The matrices MUST have the
same dimensions!
Matrix Multiplication
4 52 1 3
1 34 2 1
2 1
A
2x33x2
1
1
2
2
2 4 1 1 3 2 2 5 1 3 3 1
4 4 2 1 1 2 4 5 2 3 1 1
15 16
20 272x2
1Multiply the elements of each row of the first matrix by the elements of each column in the second matrix. 2Add the products. 3The answer goes into arow of 1st, column of 2nd.
a1,1 a1,2
a2,1 a2,2
Matrix Multiplication
Can we multiply these…
8
8 .1 2 5 2
0 1 52 2 0
8 17 5 5 9
4
4 5
7 2 .75 1 3
2 1
2 1 3 8 7
4 2 1 5 2
?
2x3 2x2 3x45x1
1x33x2
# of columns in 1st MUST be the
same as # of rows in 2nd!
No No
Yes
Matrix Multiplication with a Context
20 25 4 2 1
15 30 6 1 3
Cars Trucks
Bull’s Eye Order
JC Nickels Department Store Order
Cars
Trucks
Wheels Seats Gas Tanks
230 65 95
240 60 105
Bull’s Eye Total Order
JC Nickels Department Store Total Order
Wheels Seats Gas Tanks
20 4 25 6 15 4 30 6
20 2 25 1 20 1 25 3 15 2 30 1 15 1 30 3
Matrices and the Calculator
Follow the link below for instructions:
http://www.cpm.org/pdfs/stuRes/A2C/chapter_07/7.3.3A.pdf
Order in Matrix Multiplication Matters
132.50
0.86 0.74 0.93 134.25
107.40
132.50
134.25 0.86 0.74 0.93
107.40
0.86 132.50 0.74 134.25 0.93 107.40
313.177
OR
113.95 98.05 123.225
115.455 99.345 124.8525
92.364 79.476 99.882
132.50 0.86134.25 0.86
107.40 0.86
132.50 0.74134.25 0.74107.40 0.74
132.50 0.93134.25 0.93107.40 0.93
Matrix Multiplication
11 16
19 28
74 78 72
72 70 66
73 74 69
5.10
4.35
7.50
15 18 18
(a)
(b)
(c)
(d)
3x3 3x3 3x3
1x3 3x3 1x3
2x2 2x2 2x2
3x3 3x1 3x1
2 2
3 3
1 1
3 3
3 3
3 3
2 2
1 1
The dimensions of a product of matrices are the # of rows of the first matrix by the # of columns of
the second matrix.
In order to multiply matrices, the # of columns in 1st matrix MUST be the same as # of
rows in 2nd Matrix.
2 3 1 2
4 5 3 4
6 4 7 5 4 3
4 8 5 4 3 3
5 6 6 4 6 6
5 34 13 0.30
4 3 3 0.45
4 6 6 0.60
6 4 7
1 1 1 4 8 5
5 6 6